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Euler's formula can be used to express sinusoidal functions in terms of complex exponentials. What is the advantage of this representation?
It simplifies calculus operations
It makes the functions periodic
What is the result when eiπ/4 is evaluated using Euler's formula?
12+i2\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}21+2i
12−i2\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}21−2i
−12+i2-\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}−21+2i
What is real part of eπi/3?
2
1/2
1
Fill in the blank
eix =
coscosx+i sinsinx
sinsinx -i coscosx
sinsinx + coscosx
What is the result when e3iπ/2 is evaluated using Euler's formula?
i
-i
Euler's formula is often used to represent complex numbers in what form?
Rectangular form
Exponential form
Trigonometric form
What is the result when ei0 is evaluated using Euler's formula?
Euler's formula is a special case of a more general mathematical principle known as what?
De Moivre's theorem
Taylor's theorem
Fermat's principle
In Euler's formula, if eix is a complex number, what is the reciprocal of this number?
eix
e-ix
ex
In Euler's formula, what does represent?
The base of the natural logarithm
The imaginary unit
The complex argument
It is done.